Further Normalization of Standardized data - ANN
Data scaling or normalization is a process of making model data in a standard format so that the training is improved, accurate, and faster.

So you just have to scale the data once. Doesn't matter what scaler you are using. Just make sure to initialize the scaler with the training data and then use the same parameters to scale the test data.

The z-score normalized data (MAX-ZS) can be used directly to train the network.